In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitud...In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitudinal strong focusing(GLSF).At present,GLSF is the most promising method for realizing high-power short-wavelength coherent radiation with mild requirements on modulation laser power.Its essence is to exploit the ultrasmall natural vertical emittance of an electron beam in a planar storage ring for efficient microbunching formation,like a partial transverse-longitudinal emittance exchange in the optical laser wavelength range.Based on an in-depth investigation of related beam physics,a solution for a GLSF SSMB storage ring that can deliver 1 kW average-power EUV light is presented.The work in this paper,such as the generalized Courant–Snyder formalism,analysis of theoretical minimum emittances,transverse-longitudinal coupling dynamics,and derivation of the bunching factor and modulation strengths for laser-induced microbunching schemes,is expected to be useful not only for the development of SSMB but also for future accelerator light sources in general that demand increasingly precise electron beam phase space manipulations.展开更多
We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor coupli...We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings.With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions.When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone.Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach.The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed.In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.展开更多
In this paper, we propose a well-designed network model with a parameter and study full and partial synchronization of the network model based on the stability analysis. The network model is composed of a star-coupled...In this paper, we propose a well-designed network model with a parameter and study full and partial synchronization of the network model based on the stability analysis. The network model is composed of a star-coupled subnetwork and a globally coupled subnetwork. By analyzing the special coupling configuration, three control schemes are obtained for synchronizing the network model. Further analysis indicates that even if the inner couplings in each subnetwork are very weak, two of the control schemes are still valid. In particular, if the outer coupling weight parameter 0 is larger than （n2 - 2n）/4, or the subnetwork size n is larger than 02, the two subnetworks with weak inner couplings can achieve synchronization. In addition, the synchronizability is independent of the network size in case of 0 〈 0 〈 n/（n ＋ 1 ）. Finally, we carry out some numerical simulations to confirm the validity of the obtained control schemes. It is worth noting that the main idea of this paper also applies to any network consisting of a dense subnetwork and a sparse network.展开更多
The splitting of one-phonon coupling states in the weakly coupling model for odd-A nuclei is studied. Matrix elements are given explicitly, and an analytical expression for the energy levels is given in a perturbation...The splitting of one-phonon coupling states in the weakly coupling model for odd-A nuclei is studied. Matrix elements are given explicitly, and an analytical expression for the energy levels is given in a perturbation approach. An application is given to ^(93)Nb and ^(51)V. A comparison between the weakly coupling model and the shell model treatment for ^(51)V is discussed.展开更多
This paper demonstrates the importance of three-dimensional(3-D)piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and stron...This paper demonstrates the importance of three-dimensional(3-D)piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator.It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects(i.e.,piezoelectric coupling effect).In addition,there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end(i.e.,3-D effect).Hence,modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices,which contributes to the accurate prediction of their behavior.展开更多
We use the Lagrangian perturbation method to investigate the properties of soliton solutions in the coupled nonlinear Schrödinger equations subject to weak dissipation.Our study reveals that the two-component sol...We use the Lagrangian perturbation method to investigate the properties of soliton solutions in the coupled nonlinear Schrödinger equations subject to weak dissipation.Our study reveals that the two-component soliton solutions act as fixed-point attractors,where the numerical evolution of the system always converges to a soliton solution,regardless of the initial conditions.Interestingly,the fixed-point attractor appears as a soliton solution with a constant sum of the two-component intensities and a fixed soliton velocity,but each component soliton does not exhibit the attractor feature if the dissipation terms are identical.This suggests that one soliton attractor in the coupled systems can correspond to a group of soliton solutions,which is different from scalar cases.Our findings could inspire further discussions on dissipative-soliton dynamics in coupled systems.展开更多
In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis ofstructure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct pi...In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis ofstructure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct piezoelectriccoupling and direct piezoelectric and circuit coupling. In the proposed method, implicit and explicit formulationsare used for strong and weak coupling, respectively. Three feasible partitioned algorithms are generated, namely(1) a strongly coupled algorithm that uses a fully implicit formulation for both types of coupling, (2) a weaklycoupled algorithm that uses a fully explicit formulation for both types of coupling, and (3) a partially stronglycoupled and partially weakly coupled algorithm that uses an implicit formulation and an explicit formulation forthe two types of coupling, respectively.Numerical examples using a piezoelectric energy harvester,which is a typicalstructure-piezoelectric-circuit coupling problem, demonstrate that the proposed method selects the most costeffectivealgorithm.展开更多
Precise energy eigenvalues of metastable bound doubly excited 1,3Fe states originating from 2 pnf(n=4–6)configuration of helium-like ions(Z=2–4)under weakly coupled plasma(WCP)environment have been estimated within ...Precise energy eigenvalues of metastable bound doubly excited 1,3Fe states originating from 2 pnf(n=4–6)configuration of helium-like ions(Z=2–4)under weakly coupled plasma(WCP)environment have been estimated within the framework of Ritz variational method.The wavefunction is expanded in explicitly correlated Hylleraas type basis set.The screened Coulomb potential is consideredas mimic the WCP environment.The atomic systems tend towards gradual instability and the number of excited metastable bound states reduces with increasing plasma strength.The wavelengths corresponding to 2 pnf(1,3F^e)→2 pnf(1,3Do)(n=4–6;n′=3–6)transitions occurring between doubly excited states of plasma embedded two-electron ions are also reported.展开更多
We study the entanglement evolution in a weakly coupled bipartite system with a large energy level difference under the influence of spin-star environments. The subsystems can be coupled to a pure state or a thermal e...We study the entanglement evolution in a weakly coupled bipartite system with a large energy level difference under the influence of spin-star environments. The subsystems can be coupled to a pure state or a thermal equilibrium state spin-star environment. Our results show that, in the case of the coupling strength being less than the energy level difference of the subsystems （weakly coupled）, the spin-star environment can always be used to assist the entanglement generation of the bipartite system.展开更多
Weak and strong coupling interactions and trapped effects have always played a significant role in understanding physical and chemical properties of materials. Triple-well anharmonic potential may be modeled for inter...Weak and strong coupling interactions and trapped effects have always played a significant role in understanding physical and chemical properties of materials. Triple-well anharmonic potential may be modeled for interpretation of energy spectra from the nuclear to macro molecular systems, and also crystalline systems. Exact periods of a trapped particle in each well of the potential are explicitly derived. For the extended Duffing system, it is predicted that infinite series of both frequency and spatial trajectory approach to exact results in the limit of weak-coupling cases (g→0).展开更多
This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is establis...This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is established using the classical Krylov-Bogoliubov theory.The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.展开更多
We proposed a fiber optic high temperature sensor based on the Mach-Zehnder interference(MZI)structure,which is composed of two lengths of multi-mode fibers(MMFs),a length of few-mode fiber(FMF)and two sections of sin...We proposed a fiber optic high temperature sensor based on the Mach-Zehnder interference(MZI)structure,which is composed of two lengths of multi-mode fibers(MMFs),a length of few-mode fiber(FMF)and two sections of single-mode fibers(SMFs).Firstly,the two sections of MMFs were spliced with two sections of SMFs.Then,the MMFs were fused to two ends of FMF to form a symmetrically structured fiber-optic MZI structure.In this structure,the MMF served as the optical mode field coupling element,and the cladding and core of the FMF are the interference arm and the reference arm of the MZI structure,respectively.We investigated the sensor's response characteristics of the temperature and strain.The experimental results indicate that the sensor is sensitive to temperature variation,and the temperature response sensitivity is up to 61.4 pm/℃ in the range of 40-250℃,while the sensor has weak strain sensitivity,its strain sensitivity is only-0.72 pm/μe in the strain range of 0-1400μe.Moreover,the sensor has good stability and repeatability.In brief,the proposed fiber optic high temperature sensor has good properties,such as high sensitivity,compact structure,good stability and repeatability,which can be used for monitoring the temperature of submerged oil electric pump units under oil wells.展开更多
Coupling diversity significantly shapes signal transmission and enhancement by modulating internal component interactions in nonlinear systems.Existing theoretical studies on coupling diversity have primarily focused ...Coupling diversity significantly shapes signal transmission and enhancement by modulating internal component interactions in nonlinear systems.Existing theoretical studies on coupling diversity have primarily focused on one-dimensional bistable systems,which are limited to single-variable scenarios and simple dynamical behaviors and thus fail to adapt to complex real-world systems or reveal multi-dimensional mechanisms.To address these limitations,the present study extends this investigation to two-dimensional globally coupled bistable systems.The research team explores the law of weak signal propagation in a globally coupled model composed of bistable oscillators,in which the coupling strength between oscillators follows a Gaussian distribution.Through dual verification via numerical simulations and analytical calculations,we confirm that when the coupling diversity is at an intermediate level,a resonance effect is induced within the system.This effect directly causes the system's dynamical properties to bifurcate into three oscillation clusters with significant differences.Such a bifurcation phenomenon can significantly amplify the system's collective response to weak external signals.Specifically,with an increase in the mean coupling strength,the peaks of the spectral amplification factor become higher,and the optimal variance exhibits a right-shifting trend.Notably,this phenomenon stably emerges across different system sizes,demonstrating the robustness of the system.This finding provides a reference for a deeper understanding of the regulatory mechanism of coupling diversity in weak signal propagation.展开更多
The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly couple...The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly coupled system with memory term is also considered,where one is a power nonlinear term and the other is a derivative nonlinear term.Upper bound lifespan estimates of solution are obtained in the sub-critical by utilizing the test function method and iteration technique.The innovation of this paper focuses on the lifespan estimates of the solutions,which extends the well-known Strauss and Glassey conjectures.展开更多
基金supported by the National Key Research and Development Program of China(No.2022YFA1603401)National Natural Science Foundation of China(Nos.12035010 and 12342501)+1 种基金Beijing Outstanding Young Scientist Program(No.JWZQ20240101006)the Tsinghua University Dushi Program.
文摘In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitudinal strong focusing(GLSF).At present,GLSF is the most promising method for realizing high-power short-wavelength coherent radiation with mild requirements on modulation laser power.Its essence is to exploit the ultrasmall natural vertical emittance of an electron beam in a planar storage ring for efficient microbunching formation,like a partial transverse-longitudinal emittance exchange in the optical laser wavelength range.Based on an in-depth investigation of related beam physics,a solution for a GLSF SSMB storage ring that can deliver 1 kW average-power EUV light is presented.The work in this paper,such as the generalized Courant–Snyder formalism,analysis of theoretical minimum emittances,transverse-longitudinal coupling dynamics,and derivation of the bunching factor and modulation strengths for laser-induced microbunching schemes,is expected to be useful not only for the development of SSMB but also for future accelerator light sources in general that demand increasingly precise electron beam phase space manipulations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11604121 and 11875126)the Natural Science Fund Project of Hunan Province,China(Grant No.2017JJ3255)+1 种基金the National College Students’ Innovation Entrepreneurship Training Program,China(Grant No.201810531014)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant No.17B212)
文摘We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings.With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions.When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone.Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach.The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed.In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11162004,10972011,and 11001069)the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LQ12A01003 and LQ12A01002)the Science Foundation of Guangxi Province,China(Grant No.2013GXNS-FAA019006)
文摘In this paper, we propose a well-designed network model with a parameter and study full and partial synchronization of the network model based on the stability analysis. The network model is composed of a star-coupled subnetwork and a globally coupled subnetwork. By analyzing the special coupling configuration, three control schemes are obtained for synchronizing the network model. Further analysis indicates that even if the inner couplings in each subnetwork are very weak, two of the control schemes are still valid. In particular, if the outer coupling weight parameter 0 is larger than （n2 - 2n）/4, or the subnetwork size n is larger than 02, the two subnetworks with weak inner couplings can achieve synchronization. In addition, the synchronizability is independent of the network size in case of 0 〈 0 〈 n/（n ＋ 1 ）. Finally, we carry out some numerical simulations to confirm the validity of the obtained control schemes. It is worth noting that the main idea of this paper also applies to any network consisting of a dense subnetwork and a sparse network.
基金Supported by the Science Fund of China National Nuclear Incorporation under Grant No.J95AY5021Fund for Excellent Young University Teachers of China National Education CommissionCao Guangbiao Foundation of Tsinghua University.
文摘The splitting of one-phonon coupling states in the weakly coupling model for odd-A nuclei is studied. Matrix elements are given explicitly, and an analytical expression for the energy levels is given in a perturbation approach. An application is given to ^(93)Nb and ^(51)V. A comparison between the weakly coupling model and the shell model treatment for ^(51)V is discussed.
基金supported by the Japan Society for the Promotion of Science under KAKENHI Grant Nos.19F19379 and 20H04199。
文摘This paper demonstrates the importance of three-dimensional(3-D)piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator.It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects(i.e.,piezoelectric coupling effect).In addition,there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end(i.e.,3-D effect).Hence,modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices,which contributes to the accurate prediction of their behavior.
基金supported by the National Natural Science Foundation of China(Contract No.12022513,12235007)the Major Basic Research Program of Natural Science of Shaanxi Province(Grant No.2018KJXX-094)
文摘We use the Lagrangian perturbation method to investigate the properties of soliton solutions in the coupled nonlinear Schrödinger equations subject to weak dissipation.Our study reveals that the two-component soliton solutions act as fixed-point attractors,where the numerical evolution of the system always converges to a soliton solution,regardless of the initial conditions.Interestingly,the fixed-point attractor appears as a soliton solution with a constant sum of the two-component intensities and a fixed soliton velocity,but each component soliton does not exhibit the attractor feature if the dissipation terms are identical.This suggests that one soliton attractor in the coupled systems can correspond to a group of soliton solutions,which is different from scalar cases.Our findings could inspire further discussions on dissipative-soliton dynamics in coupled systems.
基金the Japan Society for the Promotion of Science,KAKENHI Grant Nos.20H04199 and 23H00475.
文摘In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis ofstructure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct piezoelectriccoupling and direct piezoelectric and circuit coupling. In the proposed method, implicit and explicit formulationsare used for strong and weak coupling, respectively. Three feasible partitioned algorithms are generated, namely(1) a strongly coupled algorithm that uses a fully implicit formulation for both types of coupling, (2) a weaklycoupled algorithm that uses a fully explicit formulation for both types of coupling, and (3) a partially stronglycoupled and partially weakly coupled algorithm that uses an implicit formulation and an explicit formulation forthe two types of coupling, respectively.Numerical examples using a piezoelectric energy harvester,which is a typicalstructure-piezoelectric-circuit coupling problem, demonstrate that the proposed method selects the most costeffectivealgorithm.
基金Supported under Grant No. EMR/2017/000737 from DST-SERB, Govt. of India, Grant No. 23(Sanc.)/ST/P/S&T/16G-35/2017 from DHESTB, Govt. of West Bengal, Indiaby the DHESTB,Govt.of West Bengal,India under Grant No.249(Sanc.)/ST/P/S&T/16G-26/2017
文摘Precise energy eigenvalues of metastable bound doubly excited 1,3Fe states originating from 2 pnf(n=4–6)configuration of helium-like ions(Z=2–4)under weakly coupled plasma(WCP)environment have been estimated within the framework of Ritz variational method.The wavefunction is expanded in explicitly correlated Hylleraas type basis set.The screened Coulomb potential is consideredas mimic the WCP environment.The atomic systems tend towards gradual instability and the number of excited metastable bound states reduces with increasing plasma strength.The wavelengths corresponding to 2 pnf(1,3F^e)→2 pnf(1,3Do)(n=4–6;n′=3–6)transitions occurring between doubly excited states of plasma embedded two-electron ions are also reported.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10905007 and 61078011)the Fundamental Research Funds for the Central Universities,China(Grant No.DUT12LK28)
文摘We study the entanglement evolution in a weakly coupled bipartite system with a large energy level difference under the influence of spin-star environments. The subsystems can be coupled to a pure state or a thermal equilibrium state spin-star environment. Our results show that, in the case of the coupling strength being less than the energy level difference of the subsystems （weakly coupled）, the spin-star environment can always be used to assist the entanglement generation of the bipartite system.
文摘Weak and strong coupling interactions and trapped effects have always played a significant role in understanding physical and chemical properties of materials. Triple-well anharmonic potential may be modeled for interpretation of energy spectra from the nuclear to macro molecular systems, and also crystalline systems. Exact periods of a trapped particle in each well of the potential are explicitly derived. For the extended Duffing system, it is predicted that infinite series of both frequency and spatial trajectory approach to exact results in the limit of weak-coupling cases (g→0).
基金supported in part by the NSFC(12171084,12326367)the Jiangsu Provincial Scientific Research Center of Applied Mathematics(BK20233002)the fundamental Research Funds for the Central Universities(RF1028623037)。
文摘This paper investigates the ergodicity and weak convergence of transition probabilities for two-dimensional stochastic primitive equations driven by multiplicative noise.The existence of invariant measures is established using the classical Krylov-Bogoliubov theory.The uniqueness of invariant measures and the weak convergence of transition probabilities are demonstrated through the application of the asymptotic coupling method and Foias-Prodi estimate.
基金supported by the Scientific Research Program Funded by Shaanxi Provincial Education Department (No.15JK1573)the Postgraduate Innovation and Practice Ability Development Fund of Xi’an Shiyou University (No.YCS21211084)。
文摘We proposed a fiber optic high temperature sensor based on the Mach-Zehnder interference(MZI)structure,which is composed of two lengths of multi-mode fibers(MMFs),a length of few-mode fiber(FMF)and two sections of single-mode fibers(SMFs).Firstly,the two sections of MMFs were spliced with two sections of SMFs.Then,the MMFs were fused to two ends of FMF to form a symmetrically structured fiber-optic MZI structure.In this structure,the MMF served as the optical mode field coupling element,and the cladding and core of the FMF are the interference arm and the reference arm of the MZI structure,respectively.We investigated the sensor's response characteristics of the temperature and strain.The experimental results indicate that the sensor is sensitive to temperature variation,and the temperature response sensitivity is up to 61.4 pm/℃ in the range of 40-250℃,while the sensor has weak strain sensitivity,its strain sensitivity is only-0.72 pm/μe in the strain range of 0-1400μe.Moreover,the sensor has good stability and repeatability.In brief,the proposed fiber optic high temperature sensor has good properties,such as high sensitivity,compact structure,good stability and repeatability,which can be used for monitoring the temperature of submerged oil electric pump units under oil wells.
基金supported by the National Natural Science Foundation of China(Grant No.12305054)the China Scholarship Council(Grant No.202306410194)the Guangdong Provincial Key Laboratory of Mathematical and Neural Dynamical Systems。
文摘Coupling diversity significantly shapes signal transmission and enhancement by modulating internal component interactions in nonlinear systems.Existing theoretical studies on coupling diversity have primarily focused on one-dimensional bistable systems,which are limited to single-variable scenarios and simple dynamical behaviors and thus fail to adapt to complex real-world systems or reveal multi-dimensional mechanisms.To address these limitations,the present study extends this investigation to two-dimensional globally coupled bistable systems.The research team explores the law of weak signal propagation in a globally coupled model composed of bistable oscillators,in which the coupling strength between oscillators follows a Gaussian distribution.Through dual verification via numerical simulations and analytical calculations,we confirm that when the coupling diversity is at an intermediate level,a resonance effect is induced within the system.This effect directly causes the system's dynamical properties to bifurcate into three oscillation clusters with significant differences.Such a bifurcation phenomenon can significantly amplify the system's collective response to weak external signals.Specifically,with an increase in the mean coupling strength,the peaks of the spectral amplification factor become higher,and the optimal variance exhibits a right-shifting trend.Notably,this phenomenon stably emerges across different system sizes,demonstrating the robustness of the system.This finding provides a reference for a deeper understanding of the regulatory mechanism of coupling diversity in weak signal propagation.
基金Supported by National Natural Science Foundation of China Under Grant(12401647)Supported by Fundamental Research Program of Shanxi Province(202203021212336)+2 种基金Taiyuan Institute of Technology Scientific Research Initial Funding(2023KJ057,2024KJ007,2024LJ005)Supported by Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi(2024L358)Youth Program of Taiyuan University(24TYQN10)。
文摘The main purpose of this paper is to investigate the singularities of solutions to the single Tricomi equation with derivative term and combined memory term.In addition,the blow-up of the solution to the weakly coupled system with memory term is also considered,where one is a power nonlinear term and the other is a derivative nonlinear term.Upper bound lifespan estimates of solution are obtained in the sub-critical by utilizing the test function method and iteration technique.The innovation of this paper focuses on the lifespan estimates of the solutions,which extends the well-known Strauss and Glassey conjectures.
